Question

Using substitution, which number from the set {8, 12, 16, 20} makes the equation x/4+2=5 true?

Responses 12 12 - no response given 20 20 - no response given 16 16 - no response given 8

Answer 1

To solve the equation \( \frac{x}{4} + 2 = 5 \) for \( x \), we can follow these steps:

1. Subtract 2 from both sides:
\[
\frac{x}{4} = 5 - 2
\]
\[
\frac{x}{4} = 3
\]

2. Multiply both sides by 4 to solve for \( x \):
\[
x = 3 \times 4
\]
\[
x = 12
\]

Now, let's check which number from the set \{8, 12, 16, 20\} makes the equation true:
- If \( x = 8 \):
\[
\frac{8}{4} + 2 = 2 + 2 = 4 \quad (\text{not true})
\]
- If \( x = 12 \):
\[
\frac{12}{4} + 2 = 3 + 2 = 5 \quad (\text{true})
\]
- If \( x = 16 \):
\[
\frac{16}{4} + 2 = 4 + 2 = 6 \quad (\text{not true})
\]
- If \( x = 20 \):
\[
\frac{20}{4} + 2 = 5 + 2 = 7 \quad (\text{not true})
\]

The number from the set that makes the equation true is **12**.